3.6 Multigrain FePt/FeRh material

As has been pointed out in Ref. [Thiele 04b], the granular structure is an important feature of FePt recording medium and must be taken into account in the simulations. To reproduce this realistic feature, we have introduced granular structure in our multiscale model. We used the parameters and dimensions of Sections 3.4 and 3.5 to construct the multigrain material.

First, we will present the simulations based on the system of Section 3.5 ( $K^{FePt} = 2 \cdot 10^7 erg/cm^3$) with the size of the FePt grain of $15 nm$, grouping together $10\times10\times10$ micromagnetic discretization units, which results in $8\times8$ grains, as shown in Fig. 3.22. Since the grain size of FeRh may be much larger than that of FePt, the FeRh medium was considered to be continuous. The easy axes of FePt grains were considered to be distributed according to a Gaussian distribution with small dispersion $5^\circ$. The intergrain exchange parameter $J_1^{FePt}$ was assumed to have a reduced value, with respect to the bulk value $J$. Fig. 3.23 represents hysteresis cycles corresponding to small, and intermediate intergrain exchange parameters and continuous FePt medium. The interfacial exchange parameter is also small in this case. The granular structure introduces additional nucleation centers so that the magnetization reversal process always starts earlier than that of the continuous medium. In the case of small intergrain exchange, the reversal process takes place ``grain by grain'', while for intermediate intergrain exchange, once started, the reversal process proceeds in one collective reversal.

Figure 3.22: Diagram showing how the film is divided into grains.

Figure: Simulated hysteresis cycles for 30 nm continuous FeRh/ 15 nm FePt granular media using multiscale model and $K^{FePt} = 2 \cdot 10^7 erg/cm^3$.

In Fig. 3.24 we present the coercivity reduction for granular and continuum medium within the multiscale and micromagnetic approaches. Again, the micromagnetic approach shows that in order to achieve a significant coercivity reduction, a large interfacial exchange is necessary, whereas the multiscale approach shows a significant coercivity reduction for interfacial exchange below $5\%$ of the bulk value. This result is independent of the presence of the granular structure in FePt with or without appreciable intergrain exchange. It is clearly seen that for intermediate exchange values $J_1^{FePt}/J$ the domain wall formed in FeRh penetrates in each grain at the same depinning field.

A remarkable reduction of the switching field (up to 20 times) could be achieved with thin hard layer (with thickness smaller than the exchange correlation length in hard material) and thick hard layer (with thickness higher than the exchange correlation length in soft material) and intermediate-to-full coupling. The reduction can be observed in the loop shown in Fig. 3.25 for an FePt thickness of 3 nm. However, this geometry also produces an effective coupling of hard grains through the exchange spring. A serious doubt may also arise on the signal-to-noise ratio in such implementation since the volume of soft material is much larger than that of the hard one.

Figure: Coercivity reduction in granular and continuous medium within micromagnetic and multiscale approaches for $K^{FePt} = 2 \cdot 10^7 erg/cm^3$ and 30 nm FeRh/ 15 nm FePt.

Figure: Hysteresis cycle of the continuous 30 nm FeRh/ granular 3 nm FePt thin film multilayer for $K^{FePt} = 2 \cdot 10^7 erg/cm^3$, $J_1^{FePt}/J=0.05$ and $J_s/J=0.1$.

Figure: Hysteresis cycle for 12 nm granular FePt (with $6 nm$ grains) / 12 nm continuous FeRh thin film with for $K^{FePt} = 7 \cdot 10^7 erg/cm^3$, and $J_s/J=0.05$ and $J_1^{FePt}/J=0.001$.

Next, we will consider a thin film with the grain described in Section 3.4 ( $K^{FePt} = 7 \cdot 10^7 erg/cm^3$) with granular structure for FePt ($6 nm$ grain size) and continuous FeRh film. The FePt medium was considered granular with grain size of $6 nm$. The system consisted of $10 \times 10$ grains with periodic boundary conditions in X and Y directions. The soft magnetic layer was considered continuous in order to consider the possible coupling of hard magnetic medium through the soft one which could potentially deteriorate the recording medium performance. Fig. 3.26 represents a hysteresis cycle of $12 nm$ FePt/ $12 nm$ FeRh thin film multilayer. For this small intergrain exchange value, distribution of switching fields has been observed suggesting the almost independent grains behavior.

Figure: Hysteresis cycles of the continuous 12 nm FeRh/ granular 3 nm FePt thin film multilayer for $K^{FePt} = 7 \cdot 10^7 erg/cm^3$ and $J_1^{FePt}/J=0.001$.

In the case where the thickness of FePt grain is 3nm, a large reduction in the coercivity of around $5$ times has been observed for interfacial exchange parameter larger than $10\%$ of the bulk value. This reduction is not as large as in Fig. 3.25 because of the difference in anisotropy value that determines a different pinning field. For small interfacial exchange value we observed again a distribution of the switching fields. However, for $J_s/J\geq0.1$ the demagnetization process of the granular medium takes place in one single jump suggesting that the reversal process is determined in this case by the depinning field of the exchange spring and not by the individual switching field of each magnetic grain. For this case the FePt grains are coupled effectively through the continuous FeRh. Finally, we consider granular FePt medium on granular FeRh medium with perfect grain matching. We should note here that as was pointed out in Ref. [Thiele 04b], the growth of such grains would present crucial difficulties. The FeRh is considered with reduced intergranular exchange parameter $J_1^{FeRh}$. Fig. 3.28 compares the loops for a thin FePt layer and continuous and granular thick FeRh layer. The granularity of FeRh, avoiding the effective coupling through the soft material, allows the distribution of the switching fields in FePt, which is reflected in the form of the hysteresis loop.

Figure: Hysteresis cycles of 12 nm FeRh continuous ( $J_1^{FeRh}/J=1$) and granular ( $J_1^{FeRh}/J=0.001$)/ granular 3 nm FePt thin film multilayer for $K^{FePt} = 7 \cdot 10^7 erg/cm^3$, $J_1^{FePt}/J=0.001$ and $J_s/J=0.4$. The grain size in FePt is $6 nm$